Operads in Higher-Dimensional Category Theory

Abstract

The purpose of this dissertation is to set up a theory of generalized operads and multicategories, and to use it as a language in which to propose a definition of weak n-category. Included is a full explanation of why the proposed definition of n-category is a reasonable one, and of what happens when n=2. Generalized operads and multicategories play other parts in higher-dimensional algebra too, some of which are outlined here: for instance, they can be used to simplify the opetopic approach to n-categories expounded by Baez, Dolan and others, and are a natural language in which to discuss enrichment of categorical structures.

viii + 127 pages

References in corpus (8)

• Homotopy Algebras for Operads
• General Operads and Multicategories
• Structures in higher-dimensional category theory
• Meromorphic tensor categories
• Generalized Enrichment for Categories and Multicategories
• Equivalence of Borcherds G-Vertex Algebras and Axiomatic Vertex Algebras
• fc-multicategories
• Relaxed multi category structure of a global category of rings and modules

Cited by in corpus (14)

• Operads in iterated monoidal categories
• Homomorphisms of higher categories
• Monads and theories
• Life-Space Foam: a Medium for Motivational and Cognitive Dynamics
• Polycategories via pseudo-distributive laws
• Comparing operadic theories of $n$-category
• Noncommutative calculus and operads
• Convex Hull Realizations of the Multiplihedra
• Quotients of the Multiplihedron as Categorified Associahedra
• CaTT contexts are finite computads
• Combinatorial n-fold monoidal categories and n-fold operads
• Combinatorial structure of type dependency
• Higher dimensional operads
• Comparing algebraic and non-algebraic foundations of $n$-category theory